math help :(

Question

2) A plane flew 5200km from london, U.K.,, to montreal Into a Headwind. With a Tailwind, the plane flew 150km/h faster on the Return trip. The total flying time from london to montreal and back was 14.5h. what was the flying speed from london to Montreal?

Answer 1

(2)

The Distance between London and Montreal is 5200 km.

Total flying time from London to Montreal and Montreal to London is 14.5 h.

Let V be the velocity travelled by the plane while travelling from London to Montreal.

In th return trip the veloicty is 150 kmph faster then Velocity = 150 + V

We know that speed = Distance/time

time = Distance/Speed.

Then Time taken to fly from London to Montreal is 5200/V

Time taken to fly from Montreal to London is 5200/(150+V)

Total Time = 5200/V + 5200/(150+V)

14.5 = 5200/V + 5200/(150+V)

Multiply each side by V(150+V)

14.5 = 5200(150 + V) + 5200V

14.5(V(150+V)) = 5200(150 + V) + 5200V

14.5(V²+150V) = 780000 + 5200V + 5200V

14.5V²+2175V = 780000 + 5200V + 5200V

14.5V²+2175V - (780000 + 5200V + 5200V) = 0

14.5V²+2175V - 780000 - 5200V - 5200V = 0

14.5V² - 8225V - 780000 = 0

Therefore the above equation is in form of Quadratic equation then the values of x are calculated using

The values of V are 650 and -82.758

Velocity cannot be negative here, so V = 650.

Therefore the flying speed from London to Montreal is 650 kmph.